{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"last_expr\"\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 变化率\n",
    "\n",
    "\n",
    "对于函数 ${y = f(x)}$ 定义变化率为：\n",
    "\n",
    "$$ roc = \\frac{\\Delta{y}}{\\Delta{x}}  $$\n",
    "\n",
    "代入函数曲线上的两点，可以计算 ${m}$ ：\n",
    "\n",
    "\\begin{equation}roc = \\frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}} \\end{equation}\n",
    "\n",
    "例如 ${f(x) = x^{2} + x}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x):\n",
    "    return (x)**2 + x\n",
    "\n",
    "x = np.array(range(0, 11))\n",
    "y = np.array([0,10])\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x, f(x), color='g')\n",
    "plt.plot(y, f(y), color='m')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 极限\n",
    "\n",
    "例：\n",
    "\\begin{equation}\\lim_{x \\to 5} f(x)\\end{equation}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureCanvasNbAgg()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib widget\n",
    "x = [*range(0,5), *np.arange(4.25, 6, 0.25), *range(6, 11)]\n",
    "y = [f(i) for i in x] \n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x,y, color='lightgrey', marker='o', markeredgecolor='green', markerfacecolor='green')\n",
    "plt.plot(5, f(5), color='red', marker='o', markersize=10)\n",
    "plt.plot(5.25, f(5.25), color='blue', marker='<', markersize=10)\n",
    "plt.plot(4.75, f(4.75), color='orange', marker='>', markersize=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "##  连续性\n",
    "\n",
    "对函数 ${g(x) = -(\\frac{12}{2x})^{2},\\;\\; x \\ne 0}$ 画出图形\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureCanvasNbAgg()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib widget\n",
    "def g(x):\n",
    "    if x != 0:\n",
    "        return -(12/(2*x))**2\n",
    "x = range(-20, 21)\n",
    "y = [g(a) for a in x]\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('g(x)')\n",
    "plt.grid()\n",
    "plt.plot(x,y, color='g')\n",
    "xy = (0,g(1))\n",
    "plt.annotate('O',xy, xytext=(-0.7, -37),fontsize=14,color='b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "函数 ${h(x) = 2\\sqrt{x},\\;\\; x \\ge 0}$ 是不连续的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "def h(x):\n",
    "    if x >= 0:\n",
    "        import numpy as np\n",
    "        return 2 * np.sqrt(x)\n",
    "\n",
    "x = range(-20, 21)\n",
    "y = [h(a) for a in x]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('h(x)')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x,y, color='g')\n",
    "plt.plot(0, h(0), color='g', marker='o', markerfacecolor='g', markersize=10)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "函数 ${\n",
    "k(x) = \\begin{cases}\n",
    "  x + 20, & \\text{if } x \\le 0, \\\\\n",
    "  x - 100, & \\text{otherwise }\\end{cases}}$ 是不连续的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "def k(x):\n",
    "    import numpy as np\n",
    "    if x <= 0:\n",
    "        return x + 20\n",
    "    else:\n",
    "        return x - 100\n",
    "\n",
    "x1 = range(-20, 1)\n",
    "x2 = range(1, 20)\n",
    "y1 = [k(i) for i in x1]\n",
    "y2 = [k(i) for i in x2]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('k(x)')\n",
    "plt.grid()\n",
    "plt.plot(x1,y1, color='g')\n",
    "plt.plot(x2,y2, color='g')\n",
    "plt.plot(0, k(0), color='g', marker='o', markerfacecolor='g', markersize=10)\n",
    "plt.plot(0, k(0.0001), color='g', marker='o', markerfacecolor='w', markersize=10)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 无穷\n",
    "\n",
    "对 \n",
    "$$d(x) = \\frac{4}{x - 25},\\;\\; x \\ne 25$$\n",
    "\n",
    "当 ${x \\to 25}$ 时:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "def d(x):\n",
    "    if x != 25:\n",
    "        return 4 / (x - 25)\n",
    "\n",
    "x = [*range(-100, 24), *np.arange(24.9, 25.2, 0.1), *range(26, 101)]\n",
    "y = [d(i) for i in x]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('d(x)')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x,y, color='purple')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\\begin{equation}\\lim_{x \\to 25^{+}} d(x) = \\infty \\end{equation}\n",
    "\n",
    "\\begin{equation}\\lim_{x \\to 25^{-}} d(x) = -\\infty \\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "对函数 ${e(x) = \\begin{cases}\n",
    "  5, & \\text{if } x = 0, \\\\\n",
    "  1 + x^{2}, & \\text{otherwise }\n",
    "\\end{cases}}$ 求 ${{x\\to0}}$ 时的极限：\n",
    "\n",
    "$$\\lim_{x \\to 0} a(x) \\ne a(0) $$\n",
    "\n",
    "$$\\lim_{x \\to 0} a(x) = 1 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "def e(x):\n",
    "    if x == 0:\n",
    "        return 5\n",
    "    else:\n",
    "        return 1 + x**2\n",
    "\n",
    "x= [-1, -0.5, -0.2, -0.1, -0.01, 0.01, 0.1, 0.2, 0.5, 1]\n",
    "y =[e(i) for i in x]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('e(x)')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x, y, color='m')\n",
    "plt.scatter(0, e(0), color='m')\n",
    "plt.plot(0, 1, color='m', marker='o', markerfacecolor='w', markersize=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "对函数 \n",
    "\n",
    "$$g(x) = \\frac{x^{2} - 1}{x - 1}, x \\ne 1$$\n",
    "\n",
    "求 ${x \\to 1}$ 时的极限：\n",
    "\n",
    "\\begin{equation}\\lim_{x \\to a} g(x) = \\frac{(x-1)(x+1)}{x - 1}\\end{equation}\n",
    "\n",
    "\\begin{equation}\\lim_{x \\to a} g(x)= x+1\\end{equation}\n",
    "\n",
    "\\begin{equation}\\lim_{x \\to 1} g(x) = 2\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "类似的，对函数\n",
    "\n",
    "\\begin{equation}h(x) = \\frac{\\sqrt{x} - 2}{x - 4}, x \\ne 4 \\text{ and } x \\ge 0\\end{equation}\n",
    "\n",
    "求 ${x \\to 4}$ 时的极限:\n",
    "\n",
    "\\begin{equation}\\lim_{x \\to a}h(x) = \\frac{1}{{\\sqrt{x} + 2}}\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}\\lim_{x \\to 4}h(x) = \\frac{1}{{\\sqrt{4} + 2}} = \\frac{1}{4}\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 极限的算术运算\n",
    "\n",
    "\\begin{equation}\\lim_{x \\to a} (j(x) + l(x)) = \\lim_{x \\to a} j(x) + \\lim_{x \\to a} l(x)\\end{equation}\n",
    "\n",
    "\\begin{equation}\\lim_{x \\to a} (j(x) - l(x)) = \\lim_{x \\to a} j(x) - \\lim_{x \\to a} l(x)\\end{equation}\n",
    "\n",
    "\\begin{equation}\\lim_{x \\to a} (j(x) \\cdot l(x)) = \\lim_{x \\to a} j(x) \\cdot \\lim_{x \\to a} l(x)\\end{equation}\n",
    "\n",
    "\\begin{equation}\\lim_{x \\to a} \\frac{j(x)}{l(x)} = \\frac{\\lim_{x \\to a} j(x)}{\\lim_{x \\to a} l(x)}\\end{equation}\n",
    "\n",
    "\\begin{equation}\\lim_{x \\to a} (j(x))^{n} = \\Big(\\lim_{x \\to a} j(x)\\Big)^{n}\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 微分和求导\n",
    "\n",
    "- 导函数的定义：\n",
    "\n",
    "\\begin{equation}\\lim_{h \\to 0} \\frac{f(x + h) - f(x)}{h} \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(x) = \\lim_{h \\to 0} \\frac{f(x + h) - f(x)}{h} \\end{equation}\n",
    "\n",
    "\\begin{equation}\\frac{d}{dx}f(x) = \\lim_{h \\to 0} \\frac{f(x + h) - f(x)}{h} \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "def f(x):\n",
    "    return x**2 + x\n",
    "\n",
    "x = list(range(0, 11))\n",
    "y = [f(i) for i in x]\n",
    "x1 = 3\n",
    "y1 = f(x1)\n",
    "h = 3\n",
    "x2 = x1+h\n",
    "y2 = f(x2)\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.grid()\n",
    "plt.plot(x,y, color='green')\n",
    "plt.scatter(x1,y1, c='red')\n",
    "plt.annotate('(x,f(x))',(x1,y1), xytext=(x1-0.5, y1+3))\n",
    "\n",
    "plt.scatter(x2,y2, c='red')\n",
    "plt.annotate('(x+h, f(x+h))',(x2,y2), xytext=(x2+0.5, y2))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### 导函数也可记为\n",
    "\n",
    "\\begin{equation}f'(\\textbf{a}) = \\lim_{h \\to 0} \\frac{f(\\textbf{a} + h) - f(\\textbf{a})}{h} \\Leftrightarrow f'(a) = \\lim_{x \\to a} \\frac{f(x) - f(a)}{x - a} \\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 求导数\n",
    "\n",
    "\\begin{equation}f(x) = x^{2} + x\\end{equation}\n",
    "\n",
    "\\begin{equation}f'(a) = \\lim_{h \\to 0} \\frac{f(a + h) - f(a)}{h} \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(\\textbf{2}) = \\lim_{h \\to 0} \\frac{f(\\textbf{2} + h) - f(\\textbf{2})}{h} \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(2) = \\lim_{h \\to 0} \\frac{((2+h)^{2} + 2 + h) - (2^{2} + 2)}{h} \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(2) = \\lim_{h \\to 0} \\frac{(h^{2} + 5h + 6) - 6}{h} = \\lim_{h \\to 0} \\frac{h^{2} + 5h}{h}  = \\lim_{h \\to 0} h + 5 = 5\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureCanvasNbAgg()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib widget\n",
    "\n",
    "def f(x):\n",
    "    return x**2 + x\n",
    "\n",
    "x = list(range(0, 11))\n",
    "y = [f(i) for i in x]\n",
    "\n",
    "x1 = 2\n",
    "y1 = f(x1)\n",
    "\n",
    "m = 5\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x,y, color='green')\n",
    "plt.scatter(x1,y1, c='red')\n",
    "plt.annotate('(x,f(x))',(x1,y1), xytext=(x1-0.5, y1+3))\n",
    "\n",
    "xMin = x1 - 5\n",
    "yMin = y1 - (5*m)\n",
    "xMax = x1 + 5\n",
    "yMax = y1 + (5*m)\n",
    "plt.plot([xMin,xMax],[yMin,yMax], color='magenta')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 求导函数\n",
    "\n",
    "\\begin{equation}f'(x) = \\lim_{h \\to 0} \\frac{f(x + h) - f(x)}{h} \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(x) = \\lim_{h \\to 0} \\frac{((x+h)^{2} + x + h) - (x^{2} + x)}{h} \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(x) = \\lim_{h \\to 0} \\frac{x^{2} + h^{2} + 2xh + x + h - x^{2} - x}{h} \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(x) = \\lim_{h \\to 0} \\frac{h^{2} + 2xh + h}{h} \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(x) = \\lim_{h \\to 0} 2x + h + 1 \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(x) = 2x + 1 \\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 可微\n",
    "\n",
    "并不是所有的函数都是可以求导函数的。\n",
    "\n",
    "可微的函数有下面的几何特征\n",
    "- 连续\n",
    "- 切线不竖直\n",
    "- 光滑\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "q(x) = \\begin{cases}\n",
    "  \\frac{40,000}{x^{2}}, & \\text{if } x < -4, \\\\\n",
    "  (x^{2} -2) \\cdot (x - 1), & \\text{if } x \\ne 0 \\text{ and } x \\ge -4 \\text{ and } x < 8, \\\\\n",
    "  (x^{2} -2), & \\text{if } x \\ne 0 \\text{ and } x \\ge 8\n",
    "\\end{cases}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "def q(x):\n",
    "    if x != 0:\n",
    "        if x < -4:\n",
    "            return 40000 / (x**2)\n",
    "        elif x < 8:\n",
    "            return (x**2 - 2) * x - 1\n",
    "        else:\n",
    "            return (x**2 - 2)\n",
    "\n",
    "x = [*range(-10, -5), -4.01]\n",
    "x2 = [*range(-4, 8), 7.9999, *range(8, 11)]\n",
    "\n",
    "y = [q(i) for i in x]\n",
    "y2 = [q(i) for i in x2]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('q(x)')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x,y, color='purple')\n",
    "plt.plot(x2,y2, color='purple')\n",
    "plt.scatter(-4,q(-4), c='red')\n",
    "plt.annotate('A (x= -4)',(-5,q(-3.9)), xytext=(-7, q(-3.9)))\n",
    "plt.scatter(0,0, c='red')\n",
    "plt.annotate('B (x= 0)',(0,0), xytext=(-1, 40))\n",
    "plt.scatter(8,q(8), c='red')\n",
    "plt.annotate('C (x= 8)',(8,q(8)), xytext=(8, 100))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- A不连续\n",
    "- B不连续\n",
    "- C不光滑"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 求导规则\n",
    "\n",
    "### 基本规则\n",
    "\\begin{equation}f(x) = \\pi \\;\\; \\therefore \\;\\; f'(x) = 0 \\end{equation}\n",
    "    \n",
    "\\begin{equation}f(x) = 2g(x) \\;\\; \\therefore \\;\\; f'(x) = 2g'(x) \\end{equation}\n",
    "\n",
    "\\begin{equation}f(x) = g(x) + h(x) \\;\\; \\therefore \\;\\; f'(x) = g'(x) + h'(x) \\end{equation}\n",
    "\n",
    "\\begin{equation}f(x) = k(x) - l(x) \\;\\; \\therefore \\;\\; f'(x) = k'(x) - l'(x) \\end{equation}\n",
    "\n",
    "\\begin{equation}\\frac{d}{dx}(2x + 6) = \\frac{d}{dx} 2x +  \\frac{d}{dx} 6 = 2\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 幂规则\n",
    "> 极其常用的规则\n",
    "\\begin{equation}f(x) = x^{n} \\;\\; \\therefore \\;\\; f'(x) = nx^{n-1}\\end{equation}\n",
    "\n",
    "例如：\n",
    "\n",
    "\\begin{equation}f(x) = x^{3} \\;\\; \\therefore \\;\\; f'(x) = 3x^{2}\\end{equation}\n",
    "\n",
    "\\begin{equation}f(x) = x^{-2} \\;\\; \\therefore \\;\\; f'(x) = -2x^{-3}\\end{equation}\n",
    "\n",
    "\\begin{equation}f(x) = x^{2} \\;\\; \\therefore \\;\\; f'(x) = 2x\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 幂规则的推导\n",
    "\n",
    "\\begin{equation}f(x) = x^{2}\\end{equation}\n",
    "\n",
    "\\begin{equation}f'(x) = \\lim_{h \\to 0} \\frac{f(x + h) - f(x)}{h} \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(x) = \\lim_{h \\to 0} \\frac{(x + h)^{2} - x^{2}}{h} \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(x) = \\lim_{h \\to 0} \\frac{x^{2} + h^{2} + 2xh - x^{2}}{h} = \\lim_{h \\to 0} \\frac{h^{2} + 2xh}{h} = \\lim_{h \\to 0} h + 2x = 2x\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 乘法规则\n",
    "\n",
    "\\begin{equation}\\frac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x) \\end{equation}\n",
    "\n",
    "例如\n",
    "\n",
    "\\begin{equation}f(x) = 2x^{2} \\end{equation}\n",
    "\n",
    "\\begin{equation}g(x) = x + 1 \\end{equation}\n",
    "\n",
    "\\begin{equation}f'(x) = 4x \\end{equation}\n",
    "\n",
    "\\begin{equation}g'(x) = 1 \\end{equation}\n",
    "\n",
    "\\begin{equation}\\frac{d}{dx}[f(x)g(x)] = (4x \\cdot (x + 1)) + (2x^{2} \\cdot 1) \\end{equation}\n",
    "\n",
    "\\begin{equation}\\frac{d}{dx}[f(x)g(x)] = 6x^{2} + 4x \\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 商数规则\n",
    "\\begin{equation}r(x) = \\frac{s(x)}{t(x)} \\end{equation}\n",
    "\n",
    "\\begin{equation}r'(x) = \\frac{s'(x)t(x) - s(x)t'(x)}{（t(x)）^{2}} \\end{equation}\n",
    "\n",
    "例如\n",
    "\n",
    "\\begin{equation}s(x) = 3x^{2} \\end{equation}\n",
    "\n",
    "\\begin{equation}t(x) = 2x\\end{equation}\n",
    "\n",
    "\\begin{equation}r'(x) = \\frac{(6x \\cdot 2x) - (3x^{2} \\cdot 2)}{（2x）^{2}} = \\frac{6x^{2}}{4x^{2}} = \\frac{3}{2}\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 链式规则 \n",
    "\n",
    "\\begin{equation}\\frac{d}{dx}[o(i(x))] = o'(i(x)) \\cdot i'(x)\\end{equation}\n",
    "\n",
    "例如\n",
    "\n",
    "\\begin{equation}i(x) = x^{2} \\end{equation}\n",
    "\n",
    "\\begin{equation}o(x) = 2x \\end{equation}\n",
    "\n",
    "\\begin{equation}o'(x) = 2,  i'(x) = 2x\\end{equation}\n",
    "\n",
    "\\begin{equation}\\frac{d}{dx}[o(i(x))] = 4x\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 极值和优化\n",
    "\n",
    "对函数${k(x) = -10x^{2} + 100x + 3}$ 有导函数：\n",
    "\n",
    "\\begin{equation}k'(x) = -20x + 100 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "def k(x):\n",
    "    return -10*(x**2) + (100*x)  + 3\n",
    "\n",
    "def kd(x):\n",
    "    return -20*x + 100\n",
    "\n",
    "x = list(range(0, 11))\n",
    "y = [k(i) for i in x]\n",
    "\n",
    "yd = [kd(i) for i in x]\n",
    "\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "plt.xlabel('x (time in seconds)')\n",
    "plt.ylabel('k(x) (height in feet)')\n",
    "plt.xticks(range(0,15, 1))\n",
    "plt.yticks(range(-200, 500, 20))\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x,y, color='green')\n",
    "\n",
    "plt.plot(x,yd, color='purple')\n",
    "\n",
    "x1 = 2\n",
    "x2 = 5\n",
    "x3 = 8\n",
    "plt.plot([x1-1,x1+1],[k(x1)-(kd(x1)),k(x1)+(kd(x1))], color='r')\n",
    "plt.plot([x2-1,x2+1],[k(x2)-(kd(x2)),k(x2)+(kd(x2))], color='r')\n",
    "plt.plot([x3-1,x3+1],[k(x3)-(kd(x3)),k(x3)+(kd(x3))], color='r')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 找最大值和最小值\n",
    "\n",
    "对 ${k(x) = -10x^{2} + 100x + 3}$ 有 ${k'(x) = -20x + 100 }$\n",
    "\n",
    "\\begin{equation}-20x + 100 = 0 \\end{equation}\n",
    "\n",
    "\\begin{equation}x = 5 \\end{equation}\n",
    "\n",
    "如果求二阶导数\n",
    "\n",
    "\\begin{equation}k'(x) = -20x + 100 \\Rightarrow k''(x) = -20\\end{equation}\n",
    "\n",
    "根据二阶导数为常量，而且是负常量，得知一阶导函数是线性下降的。导函数为0的点就是极大值。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "函数\n",
    "\\begin{equation}w(x) = x^{2} + 2x + 7 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "def w(x):\n",
    "    return (x**2) + (2*x) + 7\n",
    "\n",
    "def wd(x):\n",
    "    return 2*x + 2\n",
    "\n",
    "x = list(range(-10, 11))\n",
    "y = [w(i) for i in x]\n",
    "\n",
    "yd = [wd(i) for i in x]\n",
    "\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('w(x)')\n",
    "plt.xticks(range(-10,15, 1))\n",
    "plt.yticks(range(-200, 500, 20))\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x,y, color='g')\n",
    "plt.plot(x,yd, color='m')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 极值点\n",
    "\n",
    "对函数\n",
    "\\begin{equation}v(x) = x^{3} - 2x + 100 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureCanvasNbAgg()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib widget\n",
    "\n",
    "def v(x):\n",
    "    return (x**3) - (2*x) + 100\n",
    "\n",
    "def vd(x):\n",
    "    return 3*(x**2) - 2\n",
    "\n",
    "x = list(range(-10, 11))\n",
    "y = [v(i) for i in x]\n",
    "\n",
    "yd = [vd(i) for i in x]\n",
    "\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('v(x)')\n",
    "plt.xticks(range(-10,15, 1))\n",
    "plt.yticks(range(-1000, 2000, 100))\n",
    "plt.grid()\n",
    "plt.plot(x,y, color='g')\n",
    "plt.plot(x,yd, color='m')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "def k(x):\n",
    "    return -10*(x**2) + (100*x)  + 3\n",
    "\n",
    "def kd(x):\n",
    "    return -20*x + 100\n",
    "\n",
    "def k2d(x):\n",
    "    return -20\n",
    "\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "x = list(range(0, 11))\n",
    "y = [k(i) for i in x]\n",
    "yd = [kd(i) for i in x]\n",
    "y2d = [k2d(i) for i in x]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('k(x)')\n",
    "plt.xticks(range(0,15, 1))\n",
    "plt.yticks(range(-200, 500, 20))\n",
    "plt.grid()\n",
    "plt.plot(x,y, color='g')\n",
    "plt.plot(x,yd, color='r')\n",
    "plt.plot(x,y2d, color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "练习：\n",
    "\n",
    "\\begin{equation}w(x) = x^{2} + 2x + 7 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "def w(x):\n",
    "    return (x**2) + (2*x) + 7\n",
    "\n",
    "def wd(x):\n",
    "    return 2*x + 2\n",
    "\n",
    "def w2d(x):\n",
    "    return 2\n",
    "\n",
    "x = list(range(-10, 11))\n",
    "y = [w(i) for i in x]\n",
    "yd = [wd(i) for i in x]\n",
    "y2d = [w2d(i) for i in x]\n",
    "\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "plt.xlabel('x (time in days)')\n",
    "plt.ylabel('w(x) (flowers)')\n",
    "plt.xticks(range(-10,15, 1))\n",
    "plt.yticks(range(-200, 500, 20))\n",
    "plt.grid()\n",
    "plt.plot(x,y, color='green')\n",
    "plt.plot(x,yd, color='purple')\n",
    "plt.plot(x,y2d, color='magenta')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 极值点不一定是最大值或者最小值\n",
    " \n",
    "\\begin{equation}v(x) = x^{3} - 6x^{2} + 12x + 2 \\end{equation}\n",
    " \n",
    "\\begin{equation}v'(x) = 3x^{2} - 12x + 12 = 0\\end{equation}\n",
    " \n",
    "${x = 2}$ 是极值点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v(2) = 10\n",
      "v'(2) = 0\n",
      "v''(2) = 0\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "def v(x):\n",
    "    return (x**3) - (6*(x**2)) + (12*x) + 2\n",
    "\n",
    "def vd(x):\n",
    "    return (3*(x**2)) - (12*x) + 12\n",
    "\n",
    "def v2d(x):\n",
    "    return (3*(2*x)) - 12\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "x = list(range(-5, 11))\n",
    "y = [v(i) for i in x]\n",
    "yd = [vd(i) for i in x]\n",
    "y2d = [v2d(i) for i in x]\n",
    "\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('v(x)')\n",
    "plt.xticks(range(-10,15, 1))\n",
    "plt.yticks(range(-2000, 2000, 50))\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x,y, color='green')\n",
    "plt.plot(x,yd, color='purple')\n",
    "plt.plot(x,y2d, color='magenta')\n",
    "plt.show()\n",
    "\n",
    "print (\"v(2) = \" + str(v(2)))\n",
    "\n",
    "print (\"v'(2) = \" + str(vd(2)))\n",
    "\n",
    "print (\"v''(2) = \" + str(v2d(2)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 优化算法\n",
    "\n",
    "- 求一阶导数\n",
    "- 求极值\n",
    "- 求二阶导数检查是否为最大值"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# 偏微分\n",
    "\n",
    "对多变量函数\n",
    "\n",
    "$$f(x,y) = x^2 + y^2$$\n",
    "\n",
    "对于变量x, 定义\n",
    "\n",
    "$$\\frac{\\partial f(x,y)}{\\partial x} = \\frac{\\partial (x^2 + y^2)}{\\partial x}$$\n",
    "\n",
    "$$\\frac{\\partial x^2}{\\partial x} = 2x，\\;\\;\\; \\frac{\\partial y^2}{\\partial x} = 0$$\n",
    "\n",
    "$$\\frac{\\partial f(x,y)}{\\partial x} = 2x + 0 = 2x$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "对于变量y\n",
    "\n",
    "$$\\frac{\\partial f(x,y)}{\\partial y} = 0 + 2y = 2y$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 计算梯度\n",
    "\n",
    "> 梯度是多唯曲面的切面\n",
    "\n",
    "$$\\frac{\\partial f(x,y)}{\\partial x} = 2x \\\\\n",
    "\\frac{\\partial f(x,y)}{\\partial y} = 2y$$\n",
    "\n",
    "梯度向量：\n",
    "$$grad(f(x,y)) =  \\vec{g(x,y)} = \\begin{bmatrix}\\frac{\\partial f(x,y)}{\\partial x} \\\\ \\frac{\\partial f(x,y)}{\\partial y} \\end{bmatrix} = \\begin{bmatrix}2x \\\\ 2y \\end{bmatrix} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x7eff11c2b5c0>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "\n",
    "el = np.arange(-5,6)\n",
    "nx, ny = np.meshgrid(el, el, sparse=False, indexing='ij')\n",
    "\n",
    "x_coord = []\n",
    "y_coord = []\n",
    "z = []\n",
    "for i in range(11):  \n",
    "    for j in range(11):\n",
    "        x_coord.append(float(-nx[i,j]))\n",
    "        y_coord.append(float(-ny[i,j]))       \n",
    "        z.append(nx[i,j]**2 + ny[i,j]**2)\n",
    "\n",
    "x_grad = [-2 * x for x in x_coord]\n",
    "y_grad = [-2 * y for y in y_coord] \n",
    "\n",
    "plt.xlim(-5.5,5.5)\n",
    "plt.ylim(-5.5,5.5)\n",
    "for x, y, xg, yg in zip(list(x_coord), list(y_coord), list(x_grad), list(y_grad)):\n",
    "    if x != 0.0 or y != 0.0: ## Avoid the zero divide when scaling the arrow\n",
    "        l = math.sqrt(xg**2 + yg**2)/2.0\n",
    "        plt.quiver(x, y, xg, yg, width = l, units = 'dots')\n",
    "\n",
    "z = np.array(z).reshape(11,11)    \n",
    "plt.contour(el, el, z)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "图例\n",
    "- 箭头是梯度方向\n",
    "- 箭头宽度代表大小\n",
    "- 梯度方向是垂直于曲面的\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 梯度下降算法\n",
    "\n",
    "1. 从一个起点开始。\n",
    "2. 计算这点的梯度。\n",
    "3. 沿着梯度方向探索一步。\n",
    "4. 判断梯度是否接近零，如果是，停止。\n",
    "5. 否则，从第2步继续。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 积分\n",
    "\n",
    "对函数 ${f(x)=x}$ 有：\n",
    "\n",
    "$$\\int f(x)\\;dx = \\frac{1}{2} x^2$$\n",
    "\n",
    "$$\\int_0^2 f(x)\\;dx = \\frac{1}{2} x^2\\ \\big|_0^2 = \\frac{4}{2} - \\frac{0}{2} = 2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.grid()\n",
    "\n",
    "def f(x):\n",
    "    return x\n",
    "\n",
    "x = range(0, 11)\n",
    "y = [f(a) for a in x]\n",
    "\n",
    "plt.plot(x,y, color='purple')\n",
    "\n",
    "section = np.arange(0, 2, 1/20)\n",
    "plt.fill_between(section,f(section), color='orange')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0\n"
     ]
    }
   ],
   "source": [
    "import scipy.integrate as integrate\n",
    "i, e = integrate.quad(lambda x: f(x), 0, 2)\n",
    "print (i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$$\\int_0^3 3x^2 + 2x + 1\\;dx = \\frac{3}{3} x^3 + \\frac{2}{2} x^2 + x\\ \\big|_0^3 \n",
    "= 27 + 9 + 3 + 0 + 0 + 0\n",
    "= 39$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Polygon\n",
    "\n",
    "\n",
    "def g(x):\n",
    "    return 3 * x**2 + 2 * x + 1\n",
    "\n",
    "x = range(0, 11)\n",
    "y = [g(a) for a in x]\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x,y, color='purple')\n",
    "ix = np.linspace(0, 3)\n",
    "iy = g(ix)\n",
    "verts = [(0, 0)] + list(zip(ix, iy)) + [(3, 0)]\n",
    "poly = Polygon(verts, facecolor='orange')\n",
    "ax.add_patch(poly)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "38.99999999999999\n",
      "4.3298697960381095e-13\n"
     ]
    }
   ],
   "source": [
    "i, e = integrate.quad(lambda x: 3 * x**2 + 2 * x + 1, 0, 3)\n",
    "print(i)\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$$\\int^{\\infty}_0 e^{-5x} dx$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral: 0.20000000000000007\n",
      "Absolute Error: 1.560666811361375e-11\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "i, e = integrate.quad(lambda x: np.exp(-x*5), 0, np.inf)\n",
    "\n",
    "print('Integral: ' + str(i))\n",
    "print('Absolute Error: ' + str(e))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$$\\int_{-\\infty}^{\\infty} \\frac{1}{2 \\pi} e^{\\frac{-x^2}{\\sqrt(2 \\pi)}} dx$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral: 1.0000004223321999\n",
      "Absolute Error: 1.0178195684846592e-08\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "norms = lambda x: np.exp(-x**2/2.0)/np.sqrt(2.0 * 3.14159)\n",
    "i, e = integrate.quad(norms, -np.inf, np.inf)\n",
    "\n",
    "print('Integral: ' + str(i))\n",
    "print('Absolute Error: ' + str(e))"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
